Summary: Firing rate of noisy integrate-and-fire neurons with synaptic current dynamics
David Andrieux*
Department of Neurobiology and Kavli Institute for Neuroscience, Yale University School of Medicine, New Haven,
Connecticut 06510, USA
Takaaki Monnai
Department of Applied Physics, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan
Received 3 April 2009; revised manuscript received 18 June 2009; published 27 August 2009
We derive analytical formulas for the firing rate of integrate-and-fire neurons endowed with realistic synaptic
dynamics. In particular, we include the possibility of multiple synaptic inputs as well as the effect of an
absolute refractory period into the description. The latter affects the firing rate through its interaction with the
synaptic dynamics.
DOI: 10.1103/PhysRevE.80.021933 PACS number s : 87.19.L , 05.40. a, 84.35. i
I. INTRODUCTION
In vivo neurons in cortical and other neural circuits expe-
rience a large background of synaptic inputs, acting as a
source of noise. Noisy inputs have an important impact on
the dynamics of neurons, making neural responses highly
variable and affecting many of their response characteristics
1­5 . A fundamental problem is thus to determine the output
statistics of the neuronal activity given an input noise statis-